We present measurements of 2$^{nd}$ order azimuthal anisotropy ($v_{2}$) at
mid-rapidity $(|y|<1.0)$ for light nuclei d, t, $^{3}$He (for $\sqrt{s_{NN}}$ =
200, 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV) and anti-nuclei $\bar{\rm d}$
($\sqrt{s_{NN}}$ = 200, 62.4, 39, 27, and 19.6 GeV) and $^{3}\bar{\rm He}$
($\sqrt{s_{NN}}$ = 200 GeV) in the STAR (Solenoidal Tracker at RHIC)
experiment. The $v_{2}$ for these light nuclei produced in heavy-ion collisions
is compared with those for p and $\bar{\rm p}$. We observe mass ordering in
nuclei $v_{2}(p_{T})$ at low transverse momenta ($p_{T}<2.0$ GeV/$c$). We also
find a centrality dependence of $v_{2}$ for d and $\bar{\rm d}$. The magnitude
of $v_{2}$ for t and $^{3}$He agree within statistical errors. Light-nuclei
$v_{2}$ are compared with predictions from a blast wave model. Atomic mass
number ($A$) scaling of light-nuclei $v_{2}(p_{T})$ seems to hold for $p_{T}/A
< 1.5$ GeV/$c$. Results on light-nuclei $v_{2}$ from a
transport-plus-coalescence model are consistent with the experimental
measurements.